Quantitative estimates for the flux of TASEP with dilute site disorder

TL;DR

This paper analyzes how dilute site disorder affects the flux in TASEP, showing a flat segment in the flux function and providing an accurate description under certain decay assumptions, using renormalization and homogenization techniques.

Contribution

It introduces a novel renormalization approach to study TASEP with dilute disorder and characterizes the flux behavior without explicit invariant measures.

Findings

Flux function exhibits a flat segment for dilute disorder

Accurate flux description under slow power tail assumptions

Uses homogenization-inspired methods and renormalization

Abstract

We prove that the flux function of the totally asymmetric simple exclusion process (TASEP) with site disorder exhibits a flat segment for sufficiently dilute disorder. For high dilution, we obtain an accurate description of the flux. The result is established undera decay assumption of the maximum current in finite boxes, which is implied in particular by a sufficiently slow power tail assumption on the disorder distribution near its minimum. To circumvent the absence of explicit invariant measures, we use an original renormalization procedure and some ideas inspired by homogenization.